Rockfish Historical Harvest Estimates

Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest and releases of rockfish in Alaska waters and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the the shortcomings of the original Howard methods as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure. The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases. As demonstrated below, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.

Issue	Howard	Bayes
Time series	1999 - present	1977 - present
Bias in SWHS	Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests.	Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases	Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data.	Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations	Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas.	Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation	Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with.	By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

Figure 1.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}) \end{equation}\].

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

   1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
   2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
   3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

• Model: LB_fit_3pH

• Model Run: HR_fitLBR_2bias_hierPcomp_3pH_CLEAN_thru2023_3e+06_7kn_2025-04-18 (Naming convention: modelname_thruYEAR_iters_rundate)

• Proportion of parmaters converged (Rhat <= 1.1): 0.9948

• See end of document for summary of unconverged parameters.

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

And black rockfish releases…

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (including yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 10.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

Figure 12.- Residuals from logbook harvests

SWHS residuals

Figure 13.- Residuals from SWHS harvests.

Figure 14.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

Figure 15.- Mean percent of harvest by charter anglers.

When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

Figure 16.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

Figure 18.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 19.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 20.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

## NULL

## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

Figure 23.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

Figure 24.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

Figure 25.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

Figure 26.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

Figure 27.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

Figure 28.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

Figure 30.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(slope|non-pelagic & non-yellowye) For release estimates

Figure 31.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.

parameter n badRhat_avg beta2_pH 2 1.266740 beta0_pelagic 2 1.149349 beta1_pelagic 3 1.148215 beta2_black 1 1.147861

parameter n badRhat_avg beta1_pH 1 1.131921 beta3_yellow 1 1.117325 beta2_yellow 1 1.111395

Table 2. Summary of unconverged parameters by area

	CI	CSEO	NSEO	PWSI	PWSO	WKMA
beta0_pelagic	0	1	0	1	0	0
beta1_pelagic	0	1	0	1	1	0
beta1_pH	0	0	0	1	0	0
beta2_black	1	0	0	0	0	0
beta2_pH	1	0	0	0	0	1
beta2_yellow	0	0	0	1	0	0
beta3_yellow	0	0	1	0	0	0

Parameter estimates:

Summary Table of Parameter Estimates

Parameter	mean	sd	Lower_CI	Median	Upper_CI
mu_bc_H[1]	-0.125	0.075	-0.261	-0.128	0.031
mu_bc_H[2]	-0.096	0.045	-0.175	-0.100	0.009
mu_bc_H[3]	-0.435	0.070	-0.566	-0.437	-0.293
mu_bc_H[4]	-0.984	0.191	-1.358	-0.982	-0.616
mu_bc_H[5]	0.941	0.972	-0.169	0.727	3.683
mu_bc_H[6]	-2.148	0.326	-2.756	-2.165	-1.490
mu_bc_H[7]	-0.461	0.109	-0.672	-0.459	-0.250
mu_bc_H[8]	0.242	0.358	-0.361	0.209	1.051
mu_bc_H[9]	-0.292	0.139	-0.564	-0.294	-0.027
mu_bc_H[10]	-0.104	0.072	-0.239	-0.106	0.044
mu_bc_H[11]	-0.123	0.037	-0.196	-0.123	-0.049
mu_bc_H[12]	-0.251	0.104	-0.476	-0.247	-0.054
mu_bc_H[13]	-0.138	0.076	-0.292	-0.138	0.012
mu_bc_H[14]	-0.306	0.096	-0.500	-0.303	-0.125
mu_bc_H[15]	-0.342	0.051	-0.439	-0.343	-0.241
mu_bc_H[16]	-0.248	0.380	-0.875	-0.277	0.624
mu_bc_R[1]	1.357	0.151	1.065	1.355	1.661
mu_bc_R[2]	1.455	0.090	1.274	1.454	1.629
mu_bc_R[3]	1.397	0.145	1.102	1.403	1.664
mu_bc_R[4]	0.901	0.198	0.488	0.915	1.262
mu_bc_R[5]	1.178	0.469	0.246	1.187	2.092
mu_bc_R[6]	-1.592	0.420	-2.442	-1.590	-0.773
mu_bc_R[7]	0.457	0.214	0.019	0.468	0.834
mu_bc_R[8]	0.556	0.193	0.156	0.560	0.916
mu_bc_R[9]	0.349	0.200	-0.089	0.361	0.713
mu_bc_R[10]	1.302	0.132	1.032	1.308	1.560
mu_bc_R[11]	1.038	0.096	0.852	1.039	1.226
mu_bc_R[12]	0.826	0.201	0.431	0.826	1.211
mu_bc_R[13]	1.028	0.104	0.823	1.030	1.232
mu_bc_R[14]	0.895	0.145	0.611	0.896	1.167
mu_bc_R[15]	0.783	0.109	0.573	0.782	0.997
mu_bc_R[16]	1.092	0.128	0.840	1.093	1.335
tau_pH[1]	5.151	0.437	4.343	5.132	6.059
tau_pH[2]	1.990	0.220	1.585	1.979	2.442
tau_pH[3]	2.130	0.217	1.730	2.122	2.575
beta0_pH[1,1]	0.564	0.176	0.215	0.566	0.893
beta0_pH[2,1]	1.364	0.175	1.000	1.369	1.702
beta0_pH[3,1]	1.419	0.205	0.991	1.439	1.752
beta0_pH[4,1]	1.562	0.230	1.054	1.581	1.962
beta0_pH[5,1]	-0.863	0.281	-1.509	-0.842	-0.388
beta0_pH[6,1]	-0.754	0.452	-1.780	-0.681	-0.097
beta0_pH[7,1]	-0.526	0.460	-1.623	-0.495	0.322
beta0_pH[8,1]	-0.671	0.296	-1.367	-0.639	-0.185
beta0_pH[9,1]	-0.662	0.267	-1.243	-0.647	-0.170
beta0_pH[10,1]	0.233	0.212	-0.217	0.245	0.614
beta0_pH[11,1]	-0.080	0.167	-0.432	-0.079	0.242
beta0_pH[12,1]	0.495	0.194	0.106	0.499	0.865
beta0_pH[13,1]	0.014	0.149	-0.272	0.015	0.295
beta0_pH[14,1]	-0.314	0.169	-0.655	-0.313	0.008
beta0_pH[15,1]	-0.024	0.181	-0.389	-0.020	0.321
beta0_pH[16,1]	-0.488	0.371	-1.389	-0.419	0.075
beta0_pH[1,2]	2.814	0.168	2.463	2.823	3.122
beta0_pH[2,2]	2.881	0.136	2.618	2.882	3.143
beta0_pH[3,2]	3.126	0.152	2.847	3.124	3.426
beta0_pH[4,2]	2.943	0.134	2.685	2.942	3.202
beta0_pH[5,2]	4.871	1.422	3.052	4.529	8.534
beta0_pH[6,2]	3.117	0.206	2.722	3.113	3.530
beta0_pH[7,2]	1.836	0.200	1.444	1.842	2.219
beta0_pH[8,2]	2.880	0.180	2.530	2.876	3.235
beta0_pH[9,2]	3.441	0.226	3.017	3.436	3.900
beta0_pH[10,2]	3.753	0.195	3.367	3.757	4.133
beta0_pH[11,2]	-4.847	0.295	-5.430	-4.839	-4.295
beta0_pH[12,2]	-4.770	0.402	-5.564	-4.766	-3.972
beta0_pH[13,2]	-4.589	0.409	-5.388	-4.595	-3.752
beta0_pH[14,2]	-5.611	0.474	-6.597	-5.593	-4.757
beta0_pH[15,2]	-4.289	0.355	-4.975	-4.292	-3.588
beta0_pH[16,2]	-4.888	0.401	-5.706	-4.880	-4.122
beta0_pH[1,3]	0.119	0.700	-1.437	0.213	1.233
beta0_pH[2,3]	2.191	0.161	1.872	2.193	2.503
beta0_pH[3,3]	2.527	0.151	2.226	2.526	2.831
beta0_pH[4,3]	2.967	0.162	2.655	2.968	3.281
beta0_pH[5,3]	2.136	1.346	0.382	1.876	5.398
beta0_pH[6,3]	0.999	0.496	-0.171	1.019	1.884
beta0_pH[7,3]	0.629	0.172	0.298	0.625	0.973
beta0_pH[8,3]	0.312	0.191	-0.060	0.317	0.691
beta0_pH[9,3]	-0.631	0.373	-1.529	-0.600	0.005
beta0_pH[10,3]	0.477	0.364	-0.377	0.513	1.088
beta0_pH[11,3]	-0.164	0.331	-0.829	-0.161	0.490
beta0_pH[12,3]	-0.859	0.361	-1.620	-0.832	-0.229
beta0_pH[13,3]	-0.129	0.313	-0.721	-0.135	0.489
beta0_pH[14,3]	-0.271	0.266	-0.783	-0.273	0.260
beta0_pH[15,3]	-0.682	0.288	-1.281	-0.668	-0.160
beta0_pH[16,3]	-0.383	0.301	-0.970	-0.395	0.227
beta1_pH[1,1]	3.041	0.325	2.476	3.020	3.755
beta1_pH[2,1]	2.166	0.273	1.681	2.143	2.772
beta1_pH[3,1]	1.981	0.325	1.463	1.946	2.657
beta1_pH[4,1]	2.414	0.397	1.837	2.361	3.398
beta1_pH[5,1]	2.297	0.356	1.716	2.262	3.103
beta1_pH[6,1]	3.882	1.070	2.349	3.660	6.436
beta1_pH[7,1]	2.664	0.901	1.020	2.604	4.822
beta1_pH[8,1]	4.097	1.045	2.655	3.862	6.680
beta1_pH[9,1]	2.338	0.358	1.717	2.311	3.130
beta1_pH[10,1]	2.400	0.290	1.874	2.387	3.003
beta1_pH[11,1]	3.259	0.210	2.856	3.256	3.690
beta1_pH[12,1]	2.547	0.226	2.118	2.545	2.980
beta1_pH[13,1]	2.963	0.217	2.550	2.962	3.397
beta1_pH[14,1]	3.419	0.219	3.004	3.416	3.862
beta1_pH[15,1]	2.523	0.225	2.090	2.522	2.970
beta1_pH[16,1]	4.134	0.678	3.182	4.021	5.799
beta1_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,2]	0.002	0.038	0.000	0.000	0.001
beta1_pH[4,2]	0.000	0.001	0.000	0.000	0.001
beta1_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[11,2]	6.689	0.330	6.046	6.679	7.363
beta1_pH[12,2]	6.435	0.467	5.524	6.417	7.409
beta1_pH[13,2]	6.963	0.446	6.092	6.968	7.839
beta1_pH[14,2]	7.255	0.491	6.368	7.238	8.280
beta1_pH[15,2]	6.772	0.388	6.002	6.781	7.517
beta1_pH[16,2]	7.478	0.440	6.625	7.467	8.354
beta1_pH[1,3]	4.124	1.585	1.696	3.875	7.658
beta1_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[5,3]	3.370	3.014	0.803	2.784	10.440
beta1_pH[6,3]	2.840	2.130	0.488	2.627	6.582
beta1_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,3]	2.734	0.342	2.072	2.729	3.410
beta1_pH[9,3]	2.743	0.440	1.995	2.712	3.740
beta1_pH[10,3]	2.902	0.438	2.172	2.852	3.934
beta1_pH[11,3]	2.742	0.392	1.995	2.734	3.542
beta1_pH[12,3]	4.107	0.446	3.292	4.098	5.034
beta1_pH[13,3]	1.715	0.337	1.032	1.721	2.365
beta1_pH[14,3]	2.507	0.336	1.846	2.498	3.186
beta1_pH[15,3]	1.968	0.311	1.383	1.962	2.579
beta1_pH[16,3]	1.798	0.330	1.148	1.797	2.433
beta2_pH[1,1]	0.485	0.131	0.290	0.466	0.785
beta2_pH[2,1]	0.578	0.325	0.251	0.519	1.259
beta2_pH[3,1]	0.661	0.510	0.234	0.553	1.827
beta2_pH[4,1]	0.489	0.304	0.192	0.437	1.043
beta2_pH[5,1]	1.480	0.976	0.246	1.339	3.866
beta2_pH[6,1]	0.182	0.063	0.091	0.173	0.332
beta2_pH[7,1]	0.055	1.746	0.000	0.000	0.107
beta2_pH[8,1]	0.241	0.095	0.119	0.226	0.465
beta2_pH[9,1]	0.433	0.202	0.181	0.394	0.914
beta2_pH[10,1]	0.617	0.290	0.284	0.557	1.356
beta2_pH[11,1]	0.786	0.207	0.482	0.756	1.305
beta2_pH[12,1]	1.354	0.477	0.732	1.259	2.483
beta2_pH[13,1]	0.752	0.235	0.415	0.713	1.305
beta2_pH[14,1]	0.831	0.206	0.525	0.802	1.340
beta2_pH[15,1]	0.817	0.315	0.420	0.758	1.557
beta2_pH[16,1]	0.380	0.178	0.167	0.327	0.843
beta2_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,2]	-2.011	1.857	-6.905	-1.501	-0.037
beta2_pH[4,2]	-2.001	1.860	-6.859	-1.518	-0.032
beta2_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[11,2]	-9.559	4.340	-20.836	-8.612	-4.082
beta2_pH[12,2]	-8.101	5.132	-20.744	-7.155	-0.998
beta2_pH[13,2]	-7.895	4.951	-19.984	-6.764	-1.685
beta2_pH[14,2]	-8.522	4.695	-20.880	-7.411	-2.551
beta2_pH[15,2]	-9.382	4.397	-20.366	-8.395	-3.719
beta2_pH[16,2]	-9.503	4.357	-20.666	-8.460	-3.888
beta2_pH[1,3]	0.405	0.894	0.101	0.193	3.370
beta2_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[5,3]	8.963	6.161	-0.182	8.245	22.982
beta2_pH[6,3]	9.074	6.136	0.220	8.228	23.043
beta2_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,3]	9.954	5.542	1.946	8.910	23.474
beta2_pH[9,3]	8.950	6.192	0.514	7.954	23.688
beta2_pH[10,3]	8.512	6.294	0.524	7.659	23.468
beta2_pH[11,3]	-2.305	2.202	-8.796	-1.678	-0.595
beta2_pH[12,3]	-2.454	2.024	-8.776	-1.862	-0.950
beta2_pH[13,3]	-2.848	2.357	-9.952	-2.080	-0.764
beta2_pH[14,3]	-2.794	2.326	-9.686	-2.046	-0.890
beta2_pH[15,3]	-2.958	2.361	-10.214	-2.201	-0.964
beta2_pH[16,3]	-2.981	2.472	-10.485	-2.161	-0.876
beta3_pH[1,1]	35.920	0.847	34.321	35.887	37.646
beta3_pH[2,1]	33.584	1.206	31.445	33.504	36.386
beta3_pH[3,1]	33.613	1.034	31.597	33.609	35.769
beta3_pH[4,1]	33.875	1.262	31.680	33.766	36.595
beta3_pH[5,1]	27.670	1.068	26.498	27.460	30.830
beta3_pH[6,1]	38.176	3.106	32.406	37.992	44.484
beta3_pH[7,1]	30.795	7.867	18.676	30.220	45.122
beta3_pH[8,1]	40.163	2.144	36.349	39.947	44.998
beta3_pH[9,1]	30.574	1.465	27.967	30.456	33.722
beta3_pH[10,1]	32.728	0.904	31.027	32.720	34.565
beta3_pH[11,1]	30.358	0.464	29.471	30.352	31.270
beta3_pH[12,1]	30.170	0.403	29.344	30.174	30.940
beta3_pH[13,1]	33.183	0.582	32.072	33.188	34.340
beta3_pH[14,1]	32.042	0.462	31.154	32.034	32.983
beta3_pH[15,1]	31.183	0.650	29.911	31.178	32.465
beta3_pH[16,1]	32.045	1.081	30.294	31.881	34.611
beta3_pH[1,2]	30.089	8.027	18.491	29.086	45.014
beta3_pH[2,2]	29.987	8.074	18.401	29.317	45.024
beta3_pH[3,2]	30.110	8.112	18.542	29.077	45.148
beta3_pH[4,2]	30.108	7.962	18.440	29.509	44.965
beta3_pH[5,2]	29.840	7.956	18.424	28.872	44.994
beta3_pH[6,2]	29.796	8.008	18.487	28.676	44.856
beta3_pH[7,2]	30.256	7.938	18.628	29.376	45.032
beta3_pH[8,2]	30.163	7.913	18.460	29.193	44.969
beta3_pH[9,2]	30.108	7.983	18.476	29.208	45.110
beta3_pH[10,2]	30.054	8.013	18.427	29.152	45.019
beta3_pH[11,2]	43.401	0.183	43.110	43.381	43.786
beta3_pH[12,2]	43.189	0.191	42.901	43.144	43.680
beta3_pH[13,2]	43.866	0.153	43.429	43.912	44.045
beta3_pH[14,2]	43.300	0.202	43.046	43.246	43.801
beta3_pH[15,2]	43.412	0.196	43.107	43.389	43.812
beta3_pH[16,2]	43.498	0.185	43.168	43.495	43.842
beta3_pH[1,3]	39.338	3.191	32.985	39.342	45.275
beta3_pH[2,3]	30.201	7.895	18.486	29.401	44.924
beta3_pH[3,3]	30.208	7.928	18.512	29.517	45.020
beta3_pH[4,3]	30.145	7.848	18.551	29.617	44.935
beta3_pH[5,3]	36.796	3.888	31.231	36.207	44.844
beta3_pH[6,3]	40.367	3.608	31.673	40.805	45.608
beta3_pH[7,3]	37.966	4.309	31.267	37.762	45.502
beta3_pH[8,3]	41.486	0.246	41.060	41.486	41.928
beta3_pH[9,3]	33.493	0.573	31.718	33.586	34.307
beta3_pH[10,3]	35.833	0.773	33.548	36.007	36.870
beta3_pH[11,3]	41.846	0.824	40.147	41.885	43.284
beta3_pH[12,3]	41.734	0.393	40.971	41.750	42.503
beta3_pH[13,3]	42.725	0.924	41.009	42.733	44.786
beta3_pH[14,3]	41.101	0.582	39.840	41.122	42.158
beta3_pH[15,3]	42.607	0.681	41.185	42.692	43.755
beta3_pH[16,3]	42.849	0.771	41.130	42.949	44.122
beta0_pelagic[1]	2.218	0.132	1.965	2.217	2.478
beta0_pelagic[2]	1.516	0.128	1.259	1.515	1.767
beta0_pelagic[3]	-0.575	0.790	-2.460	-0.432	0.538
beta0_pelagic[4]	-0.321	0.781	-2.133	-0.101	0.768
beta0_pelagic[5]	1.190	0.254	0.638	1.192	1.665
beta0_pelagic[6]	1.472	0.272	0.884	1.493	1.966
beta0_pelagic[7]	1.591	0.208	1.187	1.590	2.024
beta0_pelagic[8]	1.761	0.207	1.370	1.755	2.196
beta0_pelagic[9]	2.490	0.306	1.893	2.497	3.061
beta0_pelagic[10]	2.541	0.200	2.143	2.541	2.929
beta0_pelagic[11]	0.116	0.414	-0.812	0.154	0.711
beta0_pelagic[12]	1.679	0.149	1.386	1.677	1.971
beta0_pelagic[13]	0.301	0.190	-0.090	0.312	0.631
beta0_pelagic[14]	-0.097	0.286	-0.741	-0.068	0.378
beta0_pelagic[15]	-0.255	0.143	-0.533	-0.252	0.034
beta0_pelagic[16]	0.284	0.283	-0.414	0.356	0.680
beta1_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[3]	2.255	1.313	0.560	2.021	5.539
beta1_pelagic[4]	1.922	1.340	0.425	1.469	5.642
beta1_pelagic[5]	-0.074	0.312	-0.685	-0.075	0.534
beta1_pelagic[6]	-0.113	0.459	-0.894	-0.177	0.731
beta1_pelagic[7]	-0.015	0.288	-0.543	-0.021	0.569
beta1_pelagic[8]	-0.007	0.279	-0.558	-0.006	0.549
beta1_pelagic[9]	0.192	0.490	-0.784	0.303	0.955
beta1_pelagic[10]	0.046	0.261	-0.465	0.043	0.564
beta1_pelagic[11]	3.522	0.999	2.150	3.337	5.678
beta1_pelagic[12]	2.760	0.323	2.151	2.751	3.415
beta1_pelagic[13]	2.941	0.673	1.821	2.860	4.475
beta1_pelagic[14]	4.306	1.029	2.808	4.130	6.686
beta1_pelagic[15]	2.923	0.258	2.439	2.921	3.434
beta1_pelagic[16]	3.625	0.883	2.672	3.305	6.022
beta2_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[3]	0.638	2.303	0.028	0.129	5.671
beta2_pelagic[4]	1.382	3.380	0.024	0.306	13.441
beta2_pelagic[5]	-0.008	0.653	-1.349	-0.006	1.356
beta2_pelagic[6]	-0.113	0.674	-1.503	-0.163	1.308
beta2_pelagic[7]	0.001	0.628	-1.275	-0.004	1.335
beta2_pelagic[8]	-0.001	0.644	-1.373	-0.002	1.364
beta2_pelagic[9]	0.186	0.674	-1.251	0.232	1.480
beta2_pelagic[10]	0.003	0.605	-1.248	0.010	1.297
beta2_pelagic[11]	1.989	4.060	0.129	0.273	14.026
beta2_pelagic[12]	5.765	4.648	0.938	4.411	18.130
beta2_pelagic[13]	0.765	1.610	0.204	0.452	3.249
beta2_pelagic[14]	0.328	0.163	0.157	0.290	0.753
beta2_pelagic[15]	5.887	4.548	1.213	4.671	18.566
beta2_pelagic[16]	4.159	4.758	0.206	2.800	17.396
beta3_pelagic[1]	29.760	7.891	18.401	28.802	45.001
beta3_pelagic[2]	29.631	7.826	18.445	28.566	44.784
beta3_pelagic[3]	29.336	6.697	18.725	28.484	43.896
beta3_pelagic[4]	25.986	5.610	18.800	24.848	42.188
beta3_pelagic[5]	30.144	8.258	18.537	28.835	45.246
beta3_pelagic[6]	31.855	6.659	19.112	31.762	44.214
beta3_pelagic[7]	29.755	8.016	18.492	28.438	45.102
beta3_pelagic[8]	29.504	7.947	18.433	28.223	44.936
beta3_pelagic[9]	30.842	6.041	19.316	30.854	42.744
beta3_pelagic[10]	29.570	8.116	18.393	28.177	45.037
beta3_pelagic[11]	42.302	2.087	36.590	42.950	45.342
beta3_pelagic[12]	43.473	0.287	42.995	43.455	44.016
beta3_pelagic[13]	42.801	1.275	40.397	42.753	45.471
beta3_pelagic[14]	42.351	1.595	39.129	42.320	45.509
beta3_pelagic[15]	43.178	0.248	42.600	43.183	43.660
beta3_pelagic[16]	43.074	0.813	40.965	43.194	44.760
mu_beta0_pelagic[1]	0.634	1.082	-1.692	0.720	2.630
mu_beta0_pelagic[2]	1.812	0.382	1.009	1.817	2.565
mu_beta0_pelagic[3]	0.316	0.467	-0.626	0.330	1.222
tau_beta0_pelagic[1]	0.461	0.534	0.049	0.283	1.910
tau_beta0_pelagic[2]	2.636	2.496	0.297	1.991	8.795
tau_beta0_pelagic[3]	1.603	1.215	0.208	1.272	4.623
beta0_yellow[1]	-0.528	0.190	-0.979	-0.509	-0.206
beta0_yellow[2]	0.483	0.198	0.080	0.500	0.789
beta0_yellow[3]	-0.331	0.194	-0.756	-0.316	0.010
beta0_yellow[4]	0.849	0.261	0.193	0.889	1.217
beta0_yellow[5]	-0.293	0.349	-0.965	-0.297	0.400
beta0_yellow[6]	1.119	0.167	0.792	1.121	1.449
beta0_yellow[7]	0.977	0.160	0.666	0.978	1.298
beta0_yellow[8]	1.009	0.154	0.707	1.007	1.303
beta0_yellow[9]	0.663	0.158	0.365	0.663	0.976
beta0_yellow[10]	0.583	0.142	0.296	0.586	0.859
beta0_yellow[11]	-1.948	0.481	-2.919	-1.938	-1.013
beta0_yellow[12]	-3.762	0.455	-4.737	-3.741	-2.921
beta0_yellow[13]	-3.761	0.489	-4.783	-3.732	-2.901
beta0_yellow[14]	-2.112	0.576	-3.148	-2.160	-0.545
beta0_yellow[15]	-2.912	0.430	-3.805	-2.898	-2.137
beta0_yellow[16]	-2.440	0.460	-3.407	-2.434	-1.538
beta1_yellow[1]	0.975	1.347	0.017	0.747	3.291
beta1_yellow[2]	1.124	0.470	0.599	1.052	2.540
beta1_yellow[3]	0.742	0.317	0.258	0.718	1.368
beta1_yellow[4]	1.373	0.717	0.637	1.190	3.596
beta1_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[11]	2.093	0.474	1.169	2.084	3.074
beta1_yellow[12]	2.556	0.467	1.702	2.530	3.546
beta1_yellow[13]	2.877	0.492	2.016	2.847	3.907
beta1_yellow[14]	2.195	0.538	0.998	2.213	3.235
beta1_yellow[15]	2.165	0.424	1.407	2.148	3.056
beta1_yellow[16]	2.197	0.459	1.316	2.190	3.165
beta2_yellow[1]	-3.345	2.900	-10.985	-2.630	-0.037
beta2_yellow[2]	-3.242	2.902	-10.850	-2.419	-0.151
beta2_yellow[3]	-2.921	2.682	-10.013	-2.213	-0.131
beta2_yellow[4]	-2.764	2.906	-10.764	-1.768	-0.109
beta2_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[11]	-4.752	2.851	-11.499	-4.099	-1.079
beta2_yellow[12]	-5.005	2.706	-11.988	-4.446	-1.462
beta2_yellow[13]	-4.917	2.619	-11.566	-4.347	-1.586
beta2_yellow[14]	-5.044	2.945	-12.268	-4.506	-0.831
beta2_yellow[15]	-4.386	2.791	-11.426	-3.675	-0.992
beta2_yellow[16]	-5.018	2.741	-11.715	-4.510	-1.359
beta3_yellow[1]	25.171	6.763	18.303	22.182	43.693
beta3_yellow[2]	29.030	1.927	24.344	28.914	32.795
beta3_yellow[3]	32.853	3.295	23.802	32.894	39.811
beta3_yellow[4]	28.856	3.344	21.759	27.977	35.760
beta3_yellow[5]	29.895	7.994	18.374	28.775	44.870
beta3_yellow[6]	30.047	8.028	18.422	29.102	45.067
beta3_yellow[7]	29.892	7.944	18.412	29.082	44.891
beta3_yellow[8]	29.985	8.020	18.515	29.103	44.799
beta3_yellow[9]	30.049	8.031	18.512	29.009	45.082
beta3_yellow[10]	29.822	7.980	18.419	28.714	44.789
beta3_yellow[11]	45.286	0.614	44.001	45.394	45.973
beta3_yellow[12]	43.311	0.372	42.574	43.288	43.991
beta3_yellow[13]	44.878	0.392	44.004	44.944	45.536
beta3_yellow[14]	43.972	1.894	35.313	44.203	45.826
beta3_yellow[15]	45.193	0.541	44.197	45.172	45.974
beta3_yellow[16]	44.554	0.664	43.378	44.555	45.819
mu_beta0_yellow[1]	0.081	0.564	-1.073	0.090	1.209
mu_beta0_yellow[2]	0.638	0.337	-0.071	0.654	1.255
mu_beta0_yellow[3]	-2.448	0.661	-3.467	-2.535	-0.876
tau_beta0_yellow[1]	1.697	1.840	0.086	1.135	6.733
tau_beta0_yellow[2]	3.504	4.246	0.345	2.374	12.863
tau_beta0_yellow[3]	1.331	1.785	0.091	0.825	5.407
beta0_black[1]	-0.079	0.162	-0.397	-0.079	0.224
beta0_black[2]	1.914	0.130	1.656	1.917	2.170
beta0_black[3]	1.314	0.133	1.052	1.316	1.572
beta0_black[4]	2.430	0.134	2.176	2.427	2.699
beta0_black[5]	1.601	1.883	-2.428	1.671	5.431
beta0_black[6]	1.601	1.931	-2.868	1.662	5.708
beta0_black[7]	1.625	1.893	-2.614	1.664	5.563
beta0_black[8]	1.302	0.226	0.868	1.299	1.758
beta0_black[9]	2.449	0.251	1.957	2.453	2.932
beta0_black[10]	1.476	0.136	1.215	1.475	1.742
beta0_black[11]	3.487	0.155	3.188	3.487	3.791
beta0_black[12]	4.865	0.174	4.525	4.861	5.217
beta0_black[13]	-0.167	0.325	-0.911	-0.132	0.292
beta0_black[14]	2.850	0.157	2.538	2.855	3.145
beta0_black[15]	1.294	0.159	0.987	1.289	1.613
beta0_black[16]	4.272	0.161	3.957	4.272	4.576
beta2_black[1]	6.251	8.504	0.517	2.781	33.765
beta2_black[2]	0.000	0.000	0.000	0.000	0.000
beta2_black[3]	0.000	0.000	0.000	0.000	0.000
beta2_black[4]	0.000	0.000	0.000	0.000	0.000
beta2_black[5]	0.000	0.000	0.000	0.000	0.000
beta2_black[6]	0.000	0.000	0.000	0.000	0.000
beta2_black[7]	0.000	0.000	0.000	0.000	0.000
beta2_black[8]	0.000	0.000	0.000	0.000	0.000
beta2_black[9]	0.000	0.000	0.000	0.000	0.000
beta2_black[10]	0.000	0.000	0.000	0.000	0.000
beta2_black[11]	0.000	0.000	0.000	0.000	0.000
beta2_black[12]	0.000	0.000	0.000	0.000	0.000
beta2_black[13]	-1.754	1.595	-6.476	-1.255	-0.174
beta2_black[14]	0.000	0.000	0.000	0.000	0.000
beta2_black[15]	0.000	0.000	0.000	0.000	0.000
beta2_black[16]	0.000	0.000	0.000	0.000	0.000
beta3_black[1]	41.760	1.233	39.690	41.922	43.345
beta3_black[2]	25.000	0.000	25.000	25.000	25.000
beta3_black[3]	25.000	0.000	25.000	25.000	25.000
beta3_black[4]	25.000	0.000	25.000	25.000	25.000
beta3_black[5]	25.000	0.000	25.000	25.000	25.000
beta3_black[6]	25.000	0.000	25.000	25.000	25.000
beta3_black[7]	25.000	0.000	25.000	25.000	25.000
beta3_black[8]	25.000	0.000	25.000	25.000	25.000
beta3_black[9]	25.000	0.000	25.000	25.000	25.000
beta3_black[10]	25.000	0.000	25.000	25.000	25.000
beta3_black[11]	25.000	0.000	25.000	25.000	25.000
beta3_black[12]	25.000	0.000	25.000	25.000	25.000
beta3_black[13]	39.069	1.358	36.022	39.288	40.713
beta3_black[14]	25.000	0.000	25.000	25.000	25.000
beta3_black[15]	25.000	0.000	25.000	25.000	25.000
beta3_black[16]	25.000	0.000	25.000	25.000	25.000
beta4_black[1]	-0.258	0.200	-0.651	-0.264	0.134
beta4_black[2]	0.242	0.185	-0.125	0.240	0.602
beta4_black[3]	-0.934	0.198	-1.324	-0.935	-0.550
beta4_black[4]	0.433	0.218	0.013	0.424	0.856
beta4_black[5]	0.245	2.548	-4.098	0.153	5.419
beta4_black[6]	0.204	2.400	-4.273	0.166	4.793
beta4_black[7]	0.240	2.511	-4.136	0.135	5.266
beta4_black[8]	-0.703	0.382	-1.470	-0.691	0.012
beta4_black[9]	1.472	1.037	-0.135	1.349	3.889
beta4_black[10]	0.025	0.194	-0.344	0.027	0.400
beta4_black[11]	-0.693	0.214	-1.104	-0.696	-0.279
beta4_black[12]	0.175	0.318	-0.425	0.171	0.804
beta4_black[13]	-1.184	0.221	-1.615	-1.185	-0.753
beta4_black[14]	-0.173	0.243	-0.641	-0.179	0.309
beta4_black[15]	-0.890	0.217	-1.315	-0.891	-0.468
beta4_black[16]	-0.595	0.238	-1.052	-0.598	-0.150
mu_beta0_black[1]	1.281	0.904	-0.718	1.329	3.023
mu_beta0_black[2]	1.596	0.879	-0.502	1.641	3.293
mu_beta0_black[3]	2.507	0.986	0.426	2.547	4.414
tau_beta0_black[1]	0.631	0.612	0.055	0.441	2.260
tau_beta0_black[2]	2.014	4.167	0.056	0.820	11.758
tau_beta0_black[3]	0.237	0.157	0.048	0.201	0.628
beta0_dsr[11]	-2.890	0.292	-3.464	-2.888	-2.333
beta0_dsr[12]	4.560	0.280	4.022	4.563	5.085
beta0_dsr[13]	-1.375	0.369	-2.112	-1.353	-0.761
beta0_dsr[14]	-3.654	0.524	-4.676	-3.652	-2.658
beta0_dsr[15]	-1.945	0.294	-2.518	-1.937	-1.391
beta0_dsr[16]	-2.991	0.371	-3.715	-2.979	-2.261
beta1_dsr[11]	4.822	0.307	4.239	4.820	5.427
beta1_dsr[12]	6.567	6.796	2.336	5.089	20.196
beta1_dsr[13]	2.900	0.442	2.262	2.854	3.919
beta1_dsr[14]	6.322	0.551	5.252	6.316	7.383
beta1_dsr[15]	3.340	0.297	2.771	3.343	3.920
beta1_dsr[16]	5.813	0.388	5.057	5.808	6.567
beta2_dsr[11]	-8.215	2.349	-13.729	-7.921	-4.564
beta2_dsr[12]	-6.985	2.634	-12.975	-6.761	-2.292
beta2_dsr[13]	-6.305	2.789	-12.208	-6.201	-0.478
beta2_dsr[14]	-6.019	2.641	-11.579	-5.941	-1.747
beta2_dsr[15]	-7.753	2.453	-13.431	-7.465	-3.842
beta2_dsr[16]	-7.873	2.333	-13.398	-7.584	-4.222
beta3_dsr[11]	43.488	0.151	43.215	43.489	43.777
beta3_dsr[12]	33.942	0.729	32.127	34.107	34.803
beta3_dsr[13]	43.260	0.372	42.797	43.202	43.908
beta3_dsr[14]	43.351	0.238	43.073	43.283	43.961
beta3_dsr[15]	43.507	0.184	43.164	43.510	43.852
beta3_dsr[16]	43.440	0.161	43.174	43.427	43.754
beta4_dsr[11]	0.586	0.218	0.170	0.577	1.017
beta4_dsr[12]	0.230	0.452	-0.675	0.229	1.144
beta4_dsr[13]	-0.168	0.222	-0.614	-0.162	0.252
beta4_dsr[14]	0.143	0.245	-0.349	0.144	0.610
beta4_dsr[15]	0.724	0.216	0.300	0.725	1.158
beta4_dsr[16]	0.146	0.234	-0.316	0.148	0.601
beta0_slope[11]	-1.851	0.146	-2.144	-1.848	-1.566
beta0_slope[12]	-5.041	1.412	-9.138	-4.533	-4.002
beta0_slope[13]	-1.341	0.191	-1.769	-1.329	-1.018
beta0_slope[14]	-2.674	0.167	-2.996	-2.678	-2.338
beta0_slope[15]	-1.345	0.146	-1.628	-1.348	-1.051
beta0_slope[16]	-2.739	0.157	-3.048	-2.737	-2.422
beta1_slope[11]	4.490	0.221	4.068	4.484	4.929
beta1_slope[12]	4.026	0.635	2.925	3.984	5.358
beta1_slope[13]	2.729	0.483	2.177	2.645	4.316
beta1_slope[14]	6.325	0.409	5.547	6.312	7.150
beta1_slope[15]	3.004	0.210	2.602	3.007	3.421
beta1_slope[16]	5.296	0.287	4.749	5.286	5.885
beta2_slope[11]	8.667	2.354	5.285	8.287	14.291
beta2_slope[12]	6.709	2.916	1.157	6.671	12.898
beta2_slope[13]	5.466	3.087	0.365	5.473	11.865
beta2_slope[14]	6.401	2.531	2.329	6.213	12.035
beta2_slope[15]	8.260	2.454	4.444	7.877	14.075
beta2_slope[16]	7.881	2.386	4.311	7.459	13.545
beta3_slope[11]	43.461	0.134	43.218	43.453	43.724
beta3_slope[12]	41.957	3.274	34.076	43.261	43.881
beta3_slope[13]	43.471	0.409	42.936	43.415	44.135
beta3_slope[14]	43.265	0.134	43.091	43.234	43.604
beta3_slope[15]	43.492	0.162	43.198	43.489	43.802
beta3_slope[16]	43.370	0.144	43.157	43.343	43.701
beta4_slope[11]	-0.721	0.160	-1.030	-0.720	-0.412
beta4_slope[12]	-1.063	0.487	-2.058	-1.047	-0.132
beta4_slope[13]	0.087	0.164	-0.228	0.086	0.415
beta4_slope[14]	-0.086	0.199	-0.476	-0.084	0.303
beta4_slope[15]	-0.757	0.157	-1.066	-0.755	-0.454
beta4_slope[16]	-0.158	0.176	-0.488	-0.161	0.195
sigma_H[1]	0.203	0.056	0.101	0.200	0.323
sigma_H[2]	0.171	0.030	0.118	0.169	0.238
sigma_H[3]	0.196	0.043	0.119	0.193	0.288
sigma_H[4]	0.422	0.076	0.296	0.414	0.594
sigma_H[5]	0.990	0.201	0.619	0.976	1.413
sigma_H[6]	0.390	0.205	0.032	0.383	0.828
sigma_H[7]	0.306	0.062	0.208	0.298	0.451
sigma_H[8]	0.417	0.090	0.278	0.408	0.604
sigma_H[9]	0.524	0.126	0.332	0.508	0.813
sigma_H[10]	0.216	0.043	0.143	0.213	0.310
sigma_H[11]	0.279	0.046	0.201	0.275	0.382
sigma_H[12]	0.437	0.164	0.209	0.413	0.765
sigma_H[13]	0.214	0.037	0.150	0.211	0.294
sigma_H[14]	0.508	0.091	0.348	0.504	0.701
sigma_H[15]	0.246	0.039	0.177	0.244	0.330
sigma_H[16]	0.225	0.044	0.155	0.221	0.324
lambda_H[1]	3.114	4.026	0.180	1.789	13.435
lambda_H[2]	8.185	7.642	0.745	6.079	29.249
lambda_H[3]	6.218	9.266	0.288	2.946	32.037
lambda_H[4]	0.006	0.004	0.001	0.005	0.018
lambda_H[5]	3.811	8.363	0.033	1.035	27.098
lambda_H[6]	7.688	15.297	0.008	0.975	46.740
lambda_H[7]	0.013	0.009	0.002	0.011	0.038
lambda_H[8]	8.108	10.074	0.103	4.654	35.965
lambda_H[9]	0.015	0.010	0.003	0.012	0.041
lambda_H[10]	0.316	0.758	0.032	0.199	1.159
lambda_H[11]	0.265	0.379	0.011	0.131	1.285
lambda_H[12]	5.050	6.646	0.183	2.742	24.731
lambda_H[13]	3.497	3.181	0.268	2.550	11.623
lambda_H[14]	3.301	4.053	0.216	2.024	13.622
lambda_H[15]	0.025	0.043	0.003	0.017	0.099
lambda_H[16]	0.817	1.176	0.043	0.426	3.945
mu_lambda_H[1]	4.340	1.919	1.193	4.130	8.547
mu_lambda_H[2]	3.850	1.931	0.651	3.710	7.839
mu_lambda_H[3]	3.549	1.870	0.766	3.256	7.825
sigma_lambda_H[1]	8.628	4.276	2.064	7.995	18.154
sigma_lambda_H[2]	8.360	4.589	1.120	7.743	18.257
sigma_lambda_H[3]	6.430	4.083	1.011	5.495	16.380
beta_H[1,1]	6.944	1.051	4.399	7.090	8.556
beta_H[2,1]	9.863	0.493	8.733	9.904	10.739
beta_H[3,1]	7.980	0.809	6.049	8.087	9.305
beta_H[4,1]	9.327	7.860	-6.692	9.641	24.462
beta_H[5,1]	0.090	2.188	-4.540	0.232	3.889
beta_H[6,1]	3.111	4.044	-6.913	4.508	7.636
beta_H[7,1]	0.422	5.825	-12.222	0.828	10.787
beta_H[8,1]	1.360	3.508	-2.250	1.257	3.610
beta_H[9,1]	13.047	5.713	2.161	13.037	24.268
beta_H[10,1]	7.030	1.726	3.234	7.157	10.102
beta_H[11,1]	5.119	3.501	-2.621	5.957	9.857
beta_H[12,1]	2.592	1.101	0.605	2.511	4.950
beta_H[13,1]	9.034	0.991	7.077	9.120	10.543
beta_H[14,1]	2.212	1.009	0.306	2.187	4.276
beta_H[15,1]	-6.035	3.743	-12.784	-6.274	1.511
beta_H[16,1]	3.546	2.675	-0.821	3.215	9.953
beta_H[1,2]	7.901	0.245	7.410	7.911	8.364
beta_H[2,2]	10.028	0.135	9.759	10.030	10.288
beta_H[3,2]	8.960	0.202	8.582	8.958	9.368
beta_H[4,2]	3.601	1.506	0.762	3.558	6.603
beta_H[5,2]	1.932	0.939	0.065	1.933	3.726
beta_H[6,2]	5.707	1.046	3.212	5.865	7.303
beta_H[7,2]	2.669	1.122	0.692	2.594	5.023
beta_H[8,2]	3.010	1.065	1.358	3.135	4.235
beta_H[9,2]	3.495	1.108	1.429	3.465	5.752
beta_H[10,2]	8.204	0.352	7.470	8.213	8.876
beta_H[11,2]	9.763	0.637	8.831	9.638	11.159
beta_H[12,2]	3.936	0.374	3.240	3.926	4.673
beta_H[13,2]	9.133	0.258	8.691	9.121	9.648
beta_H[14,2]	4.020	0.347	3.359	4.017	4.718
beta_H[15,2]	11.344	0.680	9.967	11.366	12.641
beta_H[16,2]	4.547	0.803	3.037	4.556	6.124
beta_H[1,3]	8.446	0.242	8.002	8.430	8.964
beta_H[2,3]	10.068	0.115	9.847	10.068	10.296
beta_H[3,3]	9.623	0.166	9.300	9.615	9.961
beta_H[4,3]	-2.556	0.892	-4.318	-2.541	-0.879
beta_H[5,3]	3.822	0.608	2.581	3.835	4.970
beta_H[6,3]	7.991	1.195	6.326	7.638	10.522
beta_H[7,3]	-2.765	0.663	-4.097	-2.747	-1.509
beta_H[8,3]	5.252	0.497	4.678	5.182	6.228
beta_H[9,3]	-2.858	0.738	-4.339	-2.831	-1.420
beta_H[10,3]	8.677	0.277	8.149	8.671	9.222
beta_H[11,3]	8.539	0.290	7.897	8.566	9.034
beta_H[12,3]	5.246	0.327	4.498	5.292	5.768
beta_H[13,3]	8.846	0.170	8.506	8.848	9.174
beta_H[14,3]	5.714	0.280	5.104	5.736	6.204
beta_H[15,3]	10.374	0.323	9.762	10.368	11.012
beta_H[16,3]	6.232	0.603	4.937	6.294	7.238
beta_H[1,4]	8.254	0.182	7.859	8.270	8.571
beta_H[2,4]	10.128	0.120	9.864	10.133	10.345
beta_H[3,4]	10.112	0.168	9.734	10.129	10.398
beta_H[4,4]	11.809	0.461	10.875	11.811	12.706
beta_H[5,4]	5.479	0.734	4.290	5.404	7.213
beta_H[6,4]	7.027	0.939	4.930	7.308	8.280
beta_H[7,4]	8.282	0.351	7.578	8.289	8.960
beta_H[8,4]	6.711	0.259	6.228	6.726	7.138
beta_H[9,4]	7.209	0.475	6.296	7.214	8.141
beta_H[10,4]	7.752	0.243	7.301	7.749	8.246
beta_H[11,4]	9.388	0.205	8.993	9.385	9.803
beta_H[12,4]	7.143	0.226	6.736	7.136	7.621
beta_H[13,4]	9.057	0.139	8.780	9.060	9.328
beta_H[14,4]	7.731	0.221	7.311	7.726	8.182
beta_H[15,4]	9.468	0.238	8.996	9.469	9.926
beta_H[16,4]	9.346	0.238	8.929	9.328	9.851
beta_H[1,5]	8.979	0.146	8.674	8.984	9.252
beta_H[2,5]	10.782	0.094	10.602	10.780	10.974
beta_H[3,5]	10.927	0.175	10.624	10.917	11.291
beta_H[4,5]	8.380	0.466	7.488	8.364	9.334
beta_H[5,5]	5.427	0.569	4.113	5.474	6.414
beta_H[6,5]	8.793	0.645	7.874	8.640	10.267
beta_H[7,5]	6.759	0.339	6.103	6.753	7.455
beta_H[8,5]	8.218	0.217	7.859	8.204	8.653
beta_H[9,5]	8.195	0.492	7.229	8.190	9.163
beta_H[10,5]	10.087	0.227	9.615	10.090	10.523
beta_H[11,5]	11.513	0.229	11.055	11.512	11.959
beta_H[12,5]	8.485	0.203	8.099	8.480	8.907
beta_H[13,5]	10.015	0.133	9.765	10.013	10.285
beta_H[14,5]	9.202	0.232	8.778	9.190	9.691
beta_H[15,5]	11.160	0.251	10.660	11.164	11.647
beta_H[16,5]	9.918	0.180	9.542	9.921	10.258
beta_H[1,6]	10.187	0.196	9.843	10.174	10.611
beta_H[2,6]	11.514	0.107	11.296	11.513	11.729
beta_H[3,6]	10.807	0.167	10.441	10.820	11.097
beta_H[4,6]	12.885	0.818	11.202	12.902	14.419
beta_H[5,6]	5.884	0.605	4.726	5.868	7.076
beta_H[6,6]	8.711	0.688	6.903	8.843	9.689
beta_H[7,6]	9.867	0.569	8.715	9.871	10.958
beta_H[8,6]	9.515	0.298	8.998	9.538	9.957
beta_H[9,6]	8.491	0.807	6.937	8.482	10.118
beta_H[10,6]	9.500	0.317	8.779	9.524	10.056
beta_H[11,6]	10.809	0.357	10.080	10.828	11.455
beta_H[12,6]	9.384	0.257	8.910	9.375	9.919
beta_H[13,6]	11.045	0.161	10.753	11.040	11.376
beta_H[14,6]	9.824	0.288	9.248	9.828	10.391
beta_H[15,6]	10.846	0.437	9.995	10.846	11.713
beta_H[16,6]	10.535	0.245	10.023	10.546	11.004
beta_H[1,7]	10.890	0.869	8.764	11.000	12.280
beta_H[2,7]	12.213	0.439	11.278	12.224	13.067
beta_H[3,7]	10.551	0.666	9.057	10.610	11.644
beta_H[4,7]	2.457	4.225	-5.894	2.405	11.261
beta_H[5,7]	6.406	1.830	3.089	6.378	10.452
beta_H[6,7]	9.711	2.432	5.056	9.558	16.212
beta_H[7,7]	10.525	2.820	4.811	10.496	16.242
beta_H[8,7]	10.967	1.109	9.464	10.913	12.643
beta_H[9,7]	4.396	4.075	-4.011	4.465	11.942
beta_H[10,7]	9.855	1.447	7.323	9.740	13.051
beta_H[11,7]	11.021	1.722	7.776	10.888	14.625
beta_H[12,7]	10.036	0.937	8.070	10.116	11.594
beta_H[13,7]	11.674	0.748	9.987	11.747	12.861
beta_H[14,7]	10.380	0.964	8.389	10.440	12.123
beta_H[15,7]	11.922	2.252	7.442	11.940	16.279
beta_H[16,7]	12.290	1.288	10.101	12.111	15.252
beta0_H[1]	8.876	12.603	-16.432	8.933	33.802
beta0_H[2]	10.785	6.420	-2.077	10.739	24.204
beta0_H[3]	9.655	9.842	-11.987	9.865	30.188
beta0_H[4]	8.580	182.635	-359.594	9.718	379.850
beta0_H[5]	3.230	25.193	-53.736	4.056	52.037
beta0_H[6]	6.891	52.584	-108.664	7.751	119.345
beta0_H[7]	1.504	131.014	-266.658	1.023	256.652
beta0_H[8]	5.770	38.471	-14.189	6.720	27.281
beta0_H[9]	3.092	128.935	-259.869	3.850	264.251
beta0_H[10]	8.912	34.467	-58.830	9.340	79.754
beta0_H[11]	10.309	48.823	-90.428	9.480	113.420
beta0_H[12]	6.805	12.800	-17.075	6.876	29.681
beta0_H[13]	9.859	10.789	-10.321	9.935	30.614
beta0_H[14]	7.407	11.862	-15.112	7.072	31.216
beta0_H[15]	7.716	103.638	-208.349	7.501	227.675
beta0_H[16]	7.189	27.161	-48.528	7.636	62.343